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  • Open Access

Determining drivers of chemical diffusion of hydrogen in the thin transition metallic glass V80Zr20

Lennart Spode, Ola Hartmann, and Gunnar K. Pálsson*

  • Division of Materials Physics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-75121 Uppsala, Sweden

  • *Contact author: gunnar.palsson@physics.uu.se
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Phys. Rev. B 112, 214209 – Published 11 December, 2025

DOI: https://doi.org/10.1103/4kq2-hn9t

Abstract

We demonstrate the feasibility of using optical transmission to determine concentration-dependent hydrogen diffusion coefficients and activation energies of thin metallic glass films over a wide range of temperatures and concentrations. The hydrogen concentration's temporal and spatial profiles are simultaneously extracted without requiring a metal-insulator transition or hydride formation. Different contributions to chemical hydrogen diffusion are quantified and compared. The concentration dependence of the activation energy is in stark contrast to the activation energy found in epitaxial vanadium films of similar thickness. The chemical diffusion is found to increase with hydrogen concentration in the glass, whereas it decreases in the crystalline case driven by differences in the activation energy at concentrations below 0.3H/M and the thermodynamic factor at concentrations above that. This technique provides detailed insight into the concentration dependence of hydrogen diffusion and constrains theories treating the correlated motion of hydrogen and short-range hydrogen-hydrogen interaction. The method can be applied to other materials that show an optical response to hydrogen uptake.

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References (43)

  1. N. Eliaz and D. Eliezer, An overview of hydrogen interaction with amorphous alloys, Adv. Perform. Mater. 6, 5 (1999).
  2. L. Huang, H. Lin, H. Wang, L. Ouyang, and M. Zhu, Amorphous alloys for hydrogen storage, J. Alloys Compd. 941, 168945 (2023).
  3. W. I. F. David, Effective hydrogen storage: A strategic chemistry challenge, Faraday Discuss. 151, 399 (2011).
  4. A. Borgschulte, The hydrogen grand challenge, Front. Energy Res. 4, 11 (2016).
  5. N. Eliaz, D. Fuks, and D. Eliezer, Non-Arrhenius behavior of the diffusion coefficient of hydrogen in amorphous metals, Mater. Lett. 39, 255 (1999).
  6. N. Eliaz, D. Fuks, and D. Eliezer, A new model for the diffusion behavior of hydrogen in metallic glasses, Acta Mater. 47, 2981 (1999).
  7. R. Kirchheim, F. Sommer, and G. Schluckebier, Hydrogen in amorphous metals–I, Acta Metall. 30, 1059 (1982).
  8. P. M. Richards, Distribution of activation energies for impurity hopping in amorphous metals, Phys. Rev. B 27, 2059 (1983).
  9. D. A. Faux and D. K. Ross, Tracer and chemical diffusion of hydrogen in BCC metals, J. Phys. C 20, 1441 (1987).
  10. H. R. Schober and A. M. Stoneham, Diffusion of hydrogen in niobium, Phys. Rev. Lett. 60, 2307 (1988).
  11. D. L. Tonks and R. N. Silver, Small-polaron models for the hydrogen-concentration dependence of hydrogen diffusion in Nb, Phys. Rev. B 26, 6455 (1982).
  12. A. Blomqvist, G. K. Pálsson, C. M. Araújo, R. Ahuja, and B. Hjörvarsson, Significance of self-trapping on hydrogen diffusion, Phys. Rev. Lett. 105, 185901 (2010).
  13. Y. Fukai, The Metal-Hydrogen System: Basic Bulk Properties (Springer, Berlin, 2005), pp. 55–90.
  14. H. Wipf, Hydrogen in Metals III: Properties and Applications (Springer, Berlin, 1997).
  15. M. Kaplan, G. K. Pálsson, D. M. Holzapfel, J. M. Schneider, and B. Hjörvarsson, Phase formation and thermal stability of amorphous ZrNbCrMo thin films, J. Non-Cryst. Solids: X 9–10, 100061 (2021).
  16. Y. Wang, G. K. Pálsson, H. Raanaei, and B. Hjörvarsson, The influence of amorphous Al2O3 coating on hydrogen uptake of materials, J. Alloys Compd. 464, L13 (2008).
  17. G. K. Pálsson, Y. Wang, D. Azofeifa, H. Raanaei, M. Sahlberg, and B. Hjörvarsson, Influence of titanium and vanadium on the hydrogen transport through amorphous alumina films, J. Alloys Compd. 494, 239 (2010).
  18. L. Mooij, T. Perkisas, G. Pálsson, H. Schreuders, M. Wolff, B. Hjörvarsson, S. Bals, and B. Dam, The effect of microstructure on the hydrogenation of Mg/Fe thin film multilayers, Int. J. Hydrogen Energy 39, 17092 (2014).
  19. M. Kaplan, J. Bylin, P. Malinovskis, R. H. Scheicher, and G. K. Pálsson, Hydrogen-induced enhancement of thermal stability in VZr(H) metallic glasses, Materialia 24, 101496 (2022).
  20. G. K. Pálsson, A. Bliersbach, M. Wolff, A. Zamani, and B. Hjörvarsson, Using light transmission to watch hydrogen diffuse, Nat. Commun. 3, 892 (2012).
  21. L. Mooij, W. Huang, S. A. Droulias, R. Johansson, O. Hartmann, X. Xin, H. Palonen, R. H. Scheicher, M. Wolff, and B. Hjörvarsson, Influence of site occupancy on diffusion of hydrogen in vanadium, Phys. Rev. B 95, 064310 (2017).
  22. W. Huang, L. P. A. Mooij, S. A. Droulias, H. Palonen, O. Hartmann, G. K. Pálsson, M. Wolff, and B. Hjörvarsson, Concentration dependence of hydrogen diffusion in clamped vanadium (0 0 1) films, J. Phys.: Condens. Matter 29, 045402 (2017).
  23. J. Bylin, R. Lindblad, L. Spode, R. H. Scheicher, and G. K. Pálsson, Influence of hydrogen on the electronic structure in the transition metallic glass V80Zr20, Phys. Rev. B 111, 035128 (2025).
  24. F. den Broeder, S. van der Molen, M. Kremers, J. Huiberts, D. Nagengast, A. van Gogh, W. Huisman, N. Koeman, B. Dam, J. Rector, S. Plota, M. Haaksma, R. Hanzen, R. Jungblut, P. Dunie, and R. Griessen, Visualization of hydrogen migration in solids using switchable mirrors, Nature (London) 394, 656 (1998).
  25. A. Remhof, S. J. van der Molen, A. Antosik, A. Dobrowolska, N. J. Koeman, and R. Griessen, Switchable mirrors for visualization and control of hydrogen diffusion in transition metals, Phys. Rev. B 66, 020101(R) (2002).
  26. M. Björck and G. Andersson, GenX: An extensible x-ray reflectivity refinement program utilizing differential evolution, J. Appl. Cryst. 40, 1174 (2007).
  27. M. Björck, Fitting with differential evolution: An introduction and evaluation, J. Appl. Cryst. 44, 1198 (2011).
  28. J. Bylin, The interaction of hydrogen with metallic glass, Ph.D. thesis, Acta Universitatis Upsaliensis, 2024, pp. 5–16.
  29. J. Bylin, V. Kapaklis, and G. K. Pálsson, Determining pair distribution functions of thin films using laboratory-based x-ray sources, J. Appl. Cryst. 57, 1373 (2024).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/4kq2-hn9t for figures illustrating the pressure composition isotherms of V0.8Zr0.2, chemical potentials, and thermodynamic factors at various temperatures; an explanation of the determination of D00; details on the sample growth; and a figure showing a representative x-ray intensity pattern of the samples, including a slab fit acquired using genx and the respective fitting parameters.
  31. G. Alefeld and J. Völkl, Hydrogen in Metals II: Application-Oriented Properties (Springer, Berlin, 1978), p. 81.
  32. J. Bylin, P. Malinovskis, A. Devishvili, R. H. Scheicher, and G. K. Pálsson, Hydrogen-induced volume changes, dipole tensor, and elastic hydrogen-hydrogen interaction in a metallic glass, Phys. Rev. B 106, 104110 (2022).
  33. A. Fick, Über diffusion, Ann. Phys. Chem. 170, 59 (1855).
  34. C. Matano, On the relation between the diffusion-coefficients and concentrations of solid metals (the nickel-copper system), Jpn. J. Phys. 8, 109 (1933).
  35. H. Stenlund, Three methods for solution of concentration dependent diffusion coefficient, Visilab Report No. 2004-03, ResearchGate (2011), doi: 10.13140/RG.2.1.5147.4006.
  36. J. Crank, The Mathematics of Diffusion, 2nd ed. (Oxford University Press, Oxford, 1975), p. 171.
  37. R. C. Bowman, A. J. Maeland, and W. K. Rhim, Proton NMR studies of hydrogen diffusion and electronic structure in crystalline and amorphous titanium-copper hydrides, Phys. Rev. B 26, 6362 (1982).
  38. R. C. Bowman, Jr., A. Attalla, A. Maeland, and W. Johnson, Hydrogen mobility in crystalline and amorphous Zr2PdHx, Solid State Commun. 47, 779 (1983).
  39. R. C. Bowman, Preparation and properties of amorphous hydrides, Mater. Sci. Forum 31, 197 (1988).
  40. Y. Fukai and S. Kazama, NMR studies of anomalous diffusion of hydrogen and phase transition in vanadium-hydrogen alloys, Acta Metall. 25, 59 (1977).
  41. J. E. Kleiner, E. H. Sevilla, and R. M. Cotts, Diffusion of hydrogen in α′−VHx, Phys. Rev. B 33, 6662 (1986).
  42. J. Bylin, The interaction of hydrogen with metallic glass, Ph.D. thesis, Acta Universitatis Upsaliensis, 2024, pp. 20–25.
  43. L. Spode, O. Hartmann, and G. K. Pálsson, Determining drivers of chemical diffusion of hydrogen in the thin transition metallic glass V80Zr20 [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.17541597.

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Phys. Rev. B 112, 214209– Published 11 December, 2025
  • Received 18 March 2025
  • Revised 16 September 2025
  • Accepted 20 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

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